Donald J. Trump is leading Senator Ted Cruz of Texas by double digits in Indiana, according to a new NBC News/Wall Street Journal/Marist poll, an ominous sign for Mr. Cruz going into the crucial primary there on Tuesday.

The new poll, released Sunday, shows Mr. Trump taking 49 percent of the vote to 34 percent for Mr. Cruz. Gov. John Kasich of Ohio, who has not been campaigning in the state by agreement with Mr. Cruz, receives 13 percent.

If Mr. Trump carries Indiana, which awards its 57 delegates to the statewide winner and to the winner of each congressional district, he will be far better positioned to clinch the Republican nomination on June 7, the last day of primary contests.

Mr. Cruz has mounted an all-out fight in Indiana — convincing Mr. Kasich to withdraw from competing there, naming Carly Fiorina as his would-be running mate at a rally in Indianapolis and criss-crossing the state.

But on Saturday he gave up a full day of Indiana politicking to appear at California’s state Republican convention with Ms. Fiorina. There, he declared that “California is going to decide this Republican primary.”

Candidates wooing local party activists often make such pronouncements, but Mr. Cruz’s trouble in Indiana — which is also reflected in private polls conducted by his campaign, according to Republicans briefed on those surveys — suggests that the remark may represent something more significant: a new rationale to remain in the race after Indiana.

Mr. Cruz’s polls show he is not trailing Mr. Trump in Indiana as badly as he was right after dropping five more states late last month, but his supporters are increasingly skeptical about their prospects in Indiana.

For his part, Mr. Cruz was asked nine times by Chuck Todd on NBC’s “Meet the Press” if he would support Mr. Trump as the nominee. The Texas senator filibustered, offering reason after reason that Mr. Trump should not be the nominee, but never directly answered the question.

Trip Gabriel contributed reporting.

Correction: May 1, 2016
Because of an editing error, an earlier version of this article misstated how delegates are awarded in the Indiana Republican state primary. Its 57 delegates are awarded to the statewide winner and to the winner of each congressional district; they are not awarded entirely to the statewide winner.